 # Intersection of Quadratic Graphs

Home > Quadratic Graphs Consider the graphs of a quadratic function and a linear function on the same set of axes. cutting2 points of intersection $b^2-4ac \gt 0$ touching1 point of intersection $b^2-4ac = 0$ missingno points of intersection $b^2-4ac \lt 0$ In the graphs meet, the coordinates of the points of intersection of the [...] # Finding Quadratics from Graphs

Home > Quadratic Graphs Example 1 Find the equation of the quadratic graph. Show Solution \begin{align} \displaystyle y &= a(x+2)(x+1) \\ 2 &= a(0+2)(0+1) &\text{substitute }(0,2)\\ 2 &= 2a \\ a &= 1 \\ y &= 1(x+2)(x+1) \\ \therefore y &= x^2+3x+2 \\ \end{align} Example 2 Find the equation of the quadratic graph. [...] # Quadratic Graphs by Completing the Square $y=(x-a)^2+b$

Home > Quadratic Graphs $$y=(x-a)^2+b$$ Example 1 Draw the graph of $y=(x-1)^2+2$. Show Solution The vertex is $(1,2)$ and the graph is concave up. Example 2 Draw the graph of $y=(x-1)^2-2$. Show Solution The vertex is $(1,-2)$ and the graph is concave up. Example 3 Draw the graph of $y=(x+1)^2+2$. Show Solution The vertex is [...] Home > Quadratic Graphs Vertex To find the coordinates of the vertex is to substitute the axis of symmetry $y=-\dfrac{b}{2a}$ into the expression of the parabola $y=ax^2+bx+c$. Example 1 Find of the vertex of $y=x^2 - 4x - 3$. Show Solution \begin{align} \displaystyle x &= -\dfrac{b}{2a} \\ &= -\dfrac{-4}{2 \times 1} \\ &= 2 [...] # Axis of Symmetry x=-\dfrac{b}{2a} Home > Quadratic Graphs Axis of Symmetry The equation of the axis of symmetry of y=ax^2+bx+c is x=-\dfrac{b}{2a}. Example 1 Find the equation of the axis of symmetry of y=x^2+4x-2. Show Solution \( \begin{align} \displaystyle x &= -\dfrac{b}{2a} \\ &= -\dfrac{4}{2 \times 1} \\ \therefore x &= -2 \\ \end{align} Example 2 Find the [...] # X-intercept Y-intercept

Home > Quadratic Graphs X-intercept Y-intercept $x$-intercepts: where $y=0$ $y$-intercept: where $x=0$ Example 1 Find the $y$-intercept of $y=x^2-3x+5$. Show Solution \begin{align} \displaystyle x &= 0 \\ y &= 0^2 - 3 \times 0 + 5 \\ \end{align} Thus $y$-intercept is $(0,5)$. Example 2 Find the $x$-intercept(s) of $y=x^2-6x+8$. Show Solution \( \begin{align} [...] # Quadratic Graph of $y=a(x-b)^2+c$ Form

Home > Quadratic Graphs $$y=a(x-b)^2+c$$ Vertex $(b,c)$ Concave up for $a \gt 0$ Concave down for $a \lt 0$ Example 1 Draw the graph of $y=(x-1)^2+2$. Show Solution $y=x^2$ is translated to the right $\rightarrow$ by $1$ unit and up $\uparrow$ by $2$ units. Example 2 Draw the graph of $y=(x-1)^2-2$. Show Solution $y=x^2$ is [...] # Quadratic Graph of $y=(x-a)^2$ Completed Square Form

Home > Quadratic Graphs Graph of $y=x^2$ Graph of $y=(x-1)^2$ Shift $y=x^2$ to the right by 1 unit. Graph of $y=(x+1)^2$ Shift $y=x^2$ to the left by 1 unit. Graph of $y=-(x-1)^2$ Shift $y=x^2$ to the right by 1 unit and reflect by $x$-axis. Graph of $y=-(x+1)^2$ Shift $y=x^2$ to the left by 1 unit [...]